If f be a function given by `f(x) = {1/(xIn2)-1/(2^x-1) ; x !=0 and 1/2 ; x=0`. Then

Show that the function f given by f(x)= {{:(x^2+2," if "x ne 0),(1," if "x=0):} is not continuous at x=0.

Deine F(x) as the product of two real functions f_1(x) = x, x in R, and f_2(x) ={ sin (1/x), if x !=0, 0 if x=0 follows : F(x) = { f_1(x).f_2(x) if x !=0, 0, if x = 0. Statement-1 : F(x) is continuous on R. Statement-2 : f_1(x) and f_2(x) are continuous on R.

If |c|le1/2 and f(x) is a differentiable function at x = 0 given by f(x)={(bsin^(-1)((c+x)/2), -1/2ltxlt0),(1/2, x=0),((e^((ax)/2)-1)/x, 0ltxlt1/2):} Find the value of 'a'

The function f(x) =(e^(1//x^(2))/(e^(1//x^(2))-1)" for "x ne 0,f(0)=1" at x =0 is"

Discuss the continuity of the function f(x) given by f(x)={2x-1,ifx<0 and 2x+1,ifxgeq0

The maximum valu of the function f(x) given by f(x)=x(x-1)^2,0ltxlt2 , is

The range of the functions f : [0,1] to R , given by f(x) = x^(3) - x^(2) + 4x + 2 sin^(-1)x , is